Step-by-step algebraic proof to solve 5x + 1 = 21, showing statements and reasons for each step.

Let's solve this step by step and fill in the reasons for each statement in the algebraic proof.

We are given:

Given: $ 5x + 1 = 21 $
Prove: $ x = 4 $

Here is the two-column proof with statements and reasons:

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Statements | Reasons

1) $ 5x + 1 = 21 $ | 1) a. Given
2) $ 5x = 20 $ | 2) b. Subtraction Property of Equality
3) $ x = 4 $ | 3) c. Division Property of Equality

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✔ Explanation:

- Step 1: The equation $ 5x + 1 = 21 $ is given, so the reason is simply Given.

- Step 2: We subtract 1 from both sides:
$$
5x + 1 - 1 = 21 - 1 \Rightarrow 5x = 20
$$
This uses the Subtraction Property of Equality, which states that if you subtract the same number from both sides of an equation, the equality is preserved.

- Step 3: We divide both sides by 5:
$$
\frac{5x}{5} = \frac{20}{5} \Rightarrow x = 4
$$
This uses the Division Property of Equality, which allows us to divide both sides of an equation by the same non-zero number.

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Final Answer:

1) a. Given
2) b. Subtraction Property of Equality
3) c. Division Property of Equality

✔ This completes the proof.